In the previous article we discussed how it is that we can use the present value function to understand what a set payment schedule is worth to us in terms of dollars today. While present value is very useful for us to compare different investment opportunities in terms of their worth to us today, the future value equation helps us to evaluate the true costs of our debts and obligations, by showing us exactly how much will be paid out in total over the course of the same payment schedule.
The future value equation is similar to the present value function, in that it requires the same information to calculate (payment amount, number of payment periods, and interest rate). That being said, the future value equation differs slightly in the way that it is calculated.
Future Value=Payments (1+Interest Rate) #PeriodsInterest Rate-1Interest Rate
Looking again at our bond that pays out $200 semi-annually for 5 years in an environment where a savings account pays out 3%/year, which we will remember had a present value of $1844.44, we can see that the equation is calculated as follows:
$2140.54=200 (1+.0015) 10.0015 -1.0015
This final value of $2140.54 tells us how much the investment opportunity will be worth at the end of its term. Note that if we now calculate what kind of returns we made on this investment using the FV and PV values we’ll get approximately 3%, which is the interest rate we used in the calculation in the first place. This is because of the way in which the functions calculate the worth of the payment schedule in terms of its most efficient price point against the interest rate.
Since the price is efficient, it will not represent a greater return than what it is calculated at. In order to find that amount, we need to manipulate the formula to solve for what the interest rate would be for various PV or FV values, which will be covered in greater detail later. Until then, here is the Excel formula that can be used to more easily calculate future values in a spreadsheet.